Abstract.Recently random Schrödinger operators based on
a discrete position space have drawn some attention. We illustrate
the applicability of these models to a physically plausible
statistical explanation of the phenomenon of superconductivity. In
particular, a physically interpretable random Schrödinger
operator for the description of a pair of electrons interacting
with a lattice of ions is introduced. The functional dependence of
the expected spectral gap of the operator on the lattice constant
is studied based on a long term computer experiment. It turns out
that the obtained function carries valuable statistical
information about the temperature of transition to
superconductivity for 24 chemical elements.